Trigonometric Identities

Geometry Level 3

True or False?

1 − cos ⁡ 2 x 2 = sin ⁡ x \quad \sqrt{ \dfrac{1 - \cos 2x}2} = \sin x is an identity for all real x x .

True False

Yash Jain by Yash Jain , 21, India

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1 solution

Yash Jain
Apr 10, 2017

1 − c o s 2 x 2 = 1 − ( 1 − 2 s i n 2 x ) 2 = 2 s i n 2 x 2 = s i n 2 x = ∣ s i n x ∣ , x ∈ R \large \sqrt{\frac{1-cos2x}{2}} = \sqrt{\frac{1-(1-2sin^2x)}{2}} = \sqrt{\frac{2sin^2x}{2}} = \sqrt{sin^2x} =|sinx| ,\quad x \in \mathbb{R}

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